All I can say is : “Setback Thermostats.”
These have no purpose if it doesn’t matter whether you keep your house at a constant temperature, or let it cool significantly when nobody is home.
It is not necessarily true that if something is sold there is an actual need for it. Only that there is a perceived need for it. For instance, does this ghost detector prove the existance of ghosts?
But in all seriousness I think everyone (including me, until I thought about it very carefully and did my little derivation) has an intuitive feeling that setting back thermostats should save energy, so it wouldn’t be too surprising if the majority of consumers, business people and even government-types were incorrect in their thinking.
The bucket is a good analogy if you remember that a full bucket loses water faster than a low-level bucket.
We are both saying heat loss is proportional to the indoor-outdoor temperature differential, but that is the reason for savings, not that you are somehow cheating the laws of thermodynamics by simply turning off your furnace. It’s not like turning of the TV to save energy–in that case it is true that it is always cheaper not to use it.
To address issues raised in other posts:
Let’s take this to a ridiculous extreme. Suppose have a month of constant 40 degree temperatures. You warm your house to 72 degrees inside, then turn the furnace off for a month. After some time the temperature of your house will come to equilibrium with the surrounding environment. During that time your house will experience, let’s say, heat loss H. After that there will be no further heat loss. Your next-door neighbor leaves his set to 72. Over the same period, your neighbor will have constant heat loss throughout the month. At the end of the month your turn your furnace back on, and you have to regenerate H amount of heat. During the month, the difference between your energy usage and your neighbor’s is exactly whatever the heat loss was from your neighbor’s house over the same period. You don’t get any benefit from the initial furnace downtime, because you buy back H when you turn it back on.
The same reasoning holds true whether you turn the furnace off for a month, a day, or a few hours.
In that case you will definitely save energy because once your house cools to ambient temperature you not losing any heat. This reasoning does not hold at all if the temperature in your house remains above ambient at all times, because the period you call “initial furnace downtime” never ends.
Except that it’s not just a Boolean switch “if T[sub]in[/sub] > T[sub]out[/sub] then lose heat else don’t lose heat”. If your house starts off at, say, 72 degrees, and it’s 40 degrees outside, then when you turn off your furnace, the temperature of your house will gradually decrease. When the temperature hits 70, the heat loss will be slightly lower than when it was 72. When it hits 69, it’ll be slower yet, and so on. By the time it gets down to 41 degrees, there will still be some heat loss, but it’ll be extremely slow, because the temperature difference is so low.
Ok, so I am at work 8-10 hours a day (depending on how well my day goes). I am also asleep roughly 6 hours of the day. When at work, nobody/nothing benefits from having the heat turned on in my apartment. I don’t need to worry about pipes freezing as they are properly insulated. I also turn the heat off when I sleep, an electric blanket and a comforter or two provides better heat for lower cost.
Considering that I am only home and in need of my gas heater for 8 hours of the day (maybe a little more if I am lucky), it seems pretty silly to run the heater for an additional 16 hours. I really, really, really doubt that, in this instance, there could be any fiscal advantage to running my heater 24/7. On the contrary, with natural gas as expensive as it is right now, it’d probably bankrupt me. I know this for a fact because, before forgetting to turn the heater off before a weekend vacation resulted in a significant increase to my month’s heating bill.
Now, to complicate matters (but retaining relevance to the OP):
Anybody can say it is cheaper to run a natural gas heater 8 hours than it is to run it 24 hours. However, during those 8 hours, I often get the urge to, gasp, leave the house! Trips to the grocery or the department store on foot usually last about 30 minutes to an hour, depending on how much shopping I do and which store I go to (and whether or not I am distracted by a kitty).
Usually, I turn the heater off for these excursions and turn it back on when I return. But would this kind of use be more wasteful than leaving it on?
I am beginning to lean toward the idea that while turning the heater off for long periods is energy efficient, constantly switching it on and off is not. This whole discussion is sounding similar to the whole computer power and leave-car-on-while-running-in-to-the-bank inquiries.
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I save even more money because only one room in my apartment is heated, which doesn’t sound like a lot, but that room is also my combination kitchen/dining room/bedroom/office. During the winter months I just avoid my living room. It’s more fun to watch TV and surf the net in bed, anyway. Heck, with my little apartment’s setup, I’m doing most everything in bed. My water heater can also be very easily switched off and on, so I turn it off when I am not at home. The dust mites and spiders don’t need hot showers anymore than they need warm air.
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First of all, furnaces don’t work this way–they’re “on” or “off”, and don’t modulate their output to keep a constant temperature.
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More importantly, the “cyclical” heating goes from low to high and back. You’re adding in the energy it takes to go from low to high temp, but you’re not subtracting out the energy not used when the temperature drops from high to low.
It seems this is one of those questions which gets asked regularly and repeatedly.
The answer is that setting back the thermostat does save money but there is nothing magical about it what really saves money is not the setting back of the thermostat, it is having the house colder (and therefore losing less heat). Trying to somehow keep the house warm while setting back the thermostat is like trying to buy a fish that is big but weighs little.
To put it another way, after a little thought: you’re adding things together that shouldn’t be added together. Draw a control volume around the house; the furnace need only replace energy that escapes out of the control volume. This energy is a function of [symbol]D[/symbol]temp between inside and outside. Higher average [symbol]D[/symbol]temp, higher energy loss, higher demands on the furnace.
So. Which scenario has the highest average [symbol]D[/symbol]temp? (which is essentially repeating what sailor, among others, said.
This. The bucket’s hole is at it’s bottom. Bernoulli’s equation holds true for the fluid analogy.
Exactly. But the neighbor will have been “wasting” energy keeping his house at 72, while my furnace wasn’t running at all.
This is true, due to radiation. Radiative heat transfer is proportional to the differences of the temperatures that have been raised to the fourth power. As long as you don’t turn up the heater to compensate, we can continue treating the question as academic. I have no idea how long it would take the walls to reach steady state, though; it would most likely have to be done empirically, though, as there are too many confounds.
What defines floor here? Is it the foundation of the house? The floorboard? The carpet? Yes, it is only an academic point, but, then, I am an academic! 
My kitchen/bedroom/office setup is about 2/3~4/5 thick tatami flooring, with a small square of hardwood and lino covering the rest (in the kitchen part). When the heater is on, the tatami is pretty warm, as is the hardwood (hardwood is right in front of the heater), but the lino is cold, as is the lone outside wall (which is 2/3 sliding glass door anyway). I define the walls as, well, the walls+doors, but, what is the floor? Lino + hardwood + tatami? Or do I count the dragons that live under the tatami? (I admit I have no idea what is under there) Or do I count both?
ETA: Oops, just reread Santo’s post. Confound those confounds! I may never know what effect this has on my heating bill!
Quoth seodoa:
The only possible downside to turning off the heat when you’re going to be leaving the house is that it might take a few minutes to get back up to comfortable temperature when you return and turn it back on. Now, if your outings are sufficiently brief, the benefit from turning off the heat might be very small, but it will always be some small benefit.
The only surface relevant in radiant heat transfer is the innermost one (when we’re speaking specifically of the house). Its finish and material type will determine its emissivity, while its temperature will define the gradient. The heat transfer between, say, the tile and the subfloor, will be purely conductive in nature. Once we get into the crawl space, there will be radiative heat transfer between the ground and the bottom of the subfloor. However, heat transfer through the ground will be purely conductive.
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ETA: Oops, just reread Santo’s post. Confound those confounds! I may never know what effect this has on my heating bill!
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It all depends on how accurate you want to be. We can do these back-of-the-envelopes in here, or we can spend dozens of hours with an expensive FEA program. However much time you’re willing to invest the problem is logarithmically* related to how good your answer is.
*I hope I used logarithmically right, I’m tired.
Quoth Chronos:
I agree. It’s like turning off your computer before leaving. Yes, the benefit is very small, but the only real drawback is you have to wait a whole couple minutes before logging onto SDMB. Considering I don’t particularly mind the cold and I am heating a very small space, I figure turning off the heat has got to be better than leaving it on.
Using gas is more expensive than not using gas. Amirite?
I know Bad Astronaut (possibly related to The Bad Astronomer?) addressed me earlier upthread (FTR, if folks ever really want to get in touch with me faster mailing is quicker, although for the last 3 days I’ve been really distracted due to Fierra’s emergency appendectomy…) but you and others have pretty much said what I would have in here.
I am always interested in these discussions b/c of my cheapness, also, GingerofthenotsoNorth.
All the cerebration is nice, but you’d think somewhere someone would to a frigging controlled study and come up with the empirical answer.
FWIW, my observations for the true cheapskates are:
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Keep the general temp low. Don’t obsess too much over the setback argument. In my personal opinion setback savings is way overrated, but that opinion is admittedly an ignorant one. Localized heat if you have to stay warm–i.e. a little radiant heater for the fat man’s chair instead of the general temp raised to 72. Bankie if he complains anyway.
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Avoid convective losses.
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High efficiency furnace.
Obviously good windows and good insulation but these are harder to justify if they are refits.
We don’t setback automatically b/c we are home all hours. We heat our 4000 sq foot home in northern Illinois on about 200 bucks worth of gas in bad months. Gas dryer too w gas fireplace for occ ambience. Our standard temp is 69; we could do a lot better but we are old and enfeebled and we are too lazy to lug around little space heaters like my mo-in-law does. I think low 60s is very doable with local heat supplements. However I personally built the house so the insulation is good, windows are the best and there is no significant convective loss.
You found your mistake: the heat to bring the house back up to the high temp isn’t heat lost; it’s heat you get back immediately when the thermostat goes to the low temp.
But this isn’t just a minor error that doesn’t affect the outcome: it’s the only term that argues in favor of keeping the heat high all the time. Without it, there’s no longer ever a case for keeping the heat high. (You basically said ‘it only affects the answer when the equation says to keep the heat high all the time’)
[Really short cycles, like, under an hour might start running into inefficiencies in the particular heating system, but as a theoretical matter, no reason not to turn temperature down except comfort while it’s heating up].
And, since you mention it, this is as good of a time as any to point out that, due to the on/off nature of furnaces, turning the thermostat up to 90F will not heat up your house any more quickly.
But it will with my multi-stage heat pump.